A Classification of Types of Probability and Theories of Probability

There are three fundamental conceptual divisions in the way that probability theory has been interpreted:

(1) the Classical interpretation;

(2) the epistemological (or epistemic) probability theory, further divided into

(i.) the logical interpretation;
(ii.) the subjective interpretation (personalism, subjective Bayesianism);
(iii.) the intersubjective interpretation;

(3) objective probability theory, further divided into

(i.) the frequency interpretation;
(ii.) the propensity interpretation.

(Gillies 2000: 2).

These are basically overarching philosophical interpretations of probability. The Classical interpretation is probably of historical interest only.

Keynes and Harold Jeffreys held the logical interpretation (2.i), which nevertheless seems widely rejected by modern philosophers of probability.

Frequency theorists include John Venn, A. N. Kolmogorov and Richard von Mises.

A subjective personalist theory of probability was developed by Bruno de Finetti, Frank P. Ramsey, and Leonard J. Savage. A decision making theory was developed from this that is still fundamental in neoclassical economics.

Regarding actual types of probability as a property and not a philosophy theory, although there are different classifications (see Appendix 1), perhaps there are two types, as argued by Rudolf Carnap and Ian Hacking:

(1) Epistemic/epistemological probability
A property of inferred propositions in inductive arguments, depending on the validity and soundness of the inductive arguments and evidence offered in support of it. It is thus a partial logical entailment. This is basically inductive probabilism.

(2) Aleatory probability
Long-run, relative frequency probabilities that are numerical values and that pertain to properties of elements of sets, classes or kinds. (McCann 1994: 27).

Basic notation to express probability is

P(h|e),
where P is the probability,
h is some hypothesis or conclusion, and
e is the evidence or premises.

This is usually read as “the probability of h given evidence e.” Numerical values for probability lie between 0 and 1.

0 denotes impossibility and 1 certainty.

Epistemic/epistemological probability is obviously strongly connected with induction, generally the following types of argument:

(1) induction by simple enumeration;
(2) argument by analogy;
(3) statistical syllogism, and
(4) induction to a particular.

While aleatory probabilities are capable of having numerical values, it seems that many types of inference from inductive arguments are not.

But even many events that look like they might have aleatory probabilities cannot yield them:

“In games of chance, scientific inference is possible because … an aggregate regularity (in fair games) is readily apparent; chance affords an objective, homogeneous, stationary series. In empirically observable series, on the other hand, series chosen from a potentially unstable natural environment, such homogeneity and regularity may not be in evidence. One cannot a priori assume stability; rather one must be alert to the possibly chaotic nature of any empirical series which may, over the short and the long run, generate patterns for which a probability distribution does not exist or one which generates no discernible pattern whatsoever.” (McCann 1994: 32–33).

For example, what use is the time series data on the average daily selling price of a stock in providing an objective numerical value for the probability that this stock will have value y on the 15 July, 2017? The answer is: it is useless.

The assumption of an objective, homogeneous, stationary process producing events or variables over time, in the past, present and future, is the ergodic hypothesis or ergodic axiom, familiar from neoclassical economics. If the relative frequencies of outcomes of some process converge over a long-run time series, then the process is ergodic (Glickman 2003: 368). But many economic phenomena are non-ergodic, and, for example, non-stationarity is a sufficient condition for non-ergodicity. Therefore objective probabilities do not exist in such processes: past and present time series data are of limited value or just useless for strict prediction or forecasts in terms of numerical value probabilities.

But probabilities – whether (1) objectively numerical or (2) inductive and non-numerical – only form a basis and criterion for decision and action, and decision making theory must be concerned with how people actually make decisions in particular situations, and avoid highly abstract, logically incoherent, and empirically false theories.

APPENDIX 1
Other systems of classifying types of probability as a property include the following:

(I.) Wesley Salmon (1967):

(1) Classical.
(2) subjective;
(3) frequency
(4) logical, and
(5) personal.

(II.) Roy Weatherford (1982):

(1) Classical.
(2) subjective/personal;
(3) frequency, and
(4) logical.

(III.) Leonard J. Savage (1972):

(1) necessarian;
(2) personalist, and
(3) frequentist.

Further Reading
Abrams, Marshall. 2012. “Mechanistic Social Probability: How individual Choices and Varying Circumstances produce Stable Social Patterns,” in Harold Kincaid (ed.), The Oxford Handbook of Philosophy of Social Science, Oxford University Press, Oxford. 184-226.

Galavotti, M. C. 2010. “Probability,” in Stathis Psillos and Martin Curd (eds.), The Routledge Companion to Philosophy of Science. Routledge, London and New York. 414-424.

Hartmann, S. and J. Sprenger, 2010. “Bayesian Epistemology,” in Sven Bernecker and Duncan Pritchard (eds.), The Routledge Companion to Epistemology. Routledge, London. 609-620.

Humphreys, Paul. 1998. “Probability, Interpretations of,” in Edward Craig (ed.), Routledge Encyclopedia of Philosophy. Volume 7, Nihilism - Quantum Mechanics. Routledge, London.

Interpretations of Probability, Stanford Encyclopedia of Philosophy, 2002 (rev. 2011)
http://plato.stanford.edu/entries/probability-interpret/

Loewer, Barry. 1998. “Probability Theory and Epistemology,” in Edward Craig (ed.), Routledge Encyclopedia of Philosophy. Volume 7, Nihilism - Quantum Mechanics. Routledge, London. 705-711.

Skyrms, B. 2010. “Probability, Theories of,” in Jonathan Dancy, Ernest Sosa, and Matthias Steup (eds.), A Companion to Epistemology (2nd edn.). Wiley-Blackwell, Oxford. 622–626.


BIBLIOGRAPHY
Gillies, Donald. 2000. Philosophical Theories of Probability. Routledge, London and New York.

Glickman, M. 2003. “Uncertainty,” in J. E. King (ed.), The Elgar Companion to Post Keynesian Economics. E. Elgar Pub., Cheltenham, UK and Northhampton, MA. 366–370.

McCann, Charles R. 1994. Probability Foundations of Economic Theory. Routledge, London.

Salmon, Wesley Charles. 1967. Foundations of Scientific Inference. University of Pittsburgh Press, Pittsburgh.

Savage, Leonard Jimmie. 1972. The Foundations of Statistics (2nd rev. edn.). Dover, New York.

Weatherford, Roy. 1982. Philosophical Foundations of Probability Theory. Routledge & Kegan Paul, London.

A Classification of Libertarianism

I have written on this subject before. But I think my earlier classification needs re-thinking. It is obvious that not all free market libertarianism is derived from neoclassical theory. The Austrians and the cult of Rand are not really based on neoclassical theory, although, paradoxically, the Hayekian version of the Austrian business cycle theory is heavily influenced by neoclassical equilibrium theory via Hayek’s use of Wicksellian monetary equilibrium analysis.

Here is an updated classification of free market libertarians:

(1) Randians

(2) Austrians

(i) the Anarcho-capitalists, like Rothbard and Hoppe;

(ii) The minimal state Austrians like Mises (with his praxeology);

(iii) Austrian supporters of Hayek’s economics, with a minimal state;

(iv) The “orthodox” Austrians who have a moderate subjectivist position (like Israel Kirzner and Roger Garrison);

(v) Austrian radical subjectivists like Ludwig Lachmann;

(3) Non-Austrian libertarians (but influenced by Austrian economics)

I suspect that it is also possible to put many of the “Free Bankers” in this category.

(4) Neoclassical libertarians (but influenced by Austrian economics and neoclassical theory)

(i) followers of Robert Nozick’s libertarianism;

(ii) followers of David D. Friedman’s anarcho-capitalism, and other non-Austrian anarcho-capitalism (e.g., Jan Narveson);

(iii) other non-Austrian, neoclassical influenced libertarians (e.g., Tom Palmer, Bryan Caplan and Tyler Cowen).

I have not included Milton Friedman’s monetarism here, because Friedman’s economics was the pretty much mainstream neoclassical macroeconomic theory. Moreover, I am not sure that all modern monetarists or new monetarists would really think of themselves as “libertarians.” Although they are supporters of free markets, I suspect many think of themselves just as mainstream economists.

UPDATE

I have taken Professor George Selgin out of category (3). Professor Selgin no longer self-identifies as an Austrian, but also notes in a comment below:

“... I am no less uncomfortable with the libertarian label than I am with the Austrian one. In fact, you will be hard-pressed to find me ever identifying with a "movement" of any sort: I dislike them all, viscerally.”
http://socialdemocracy21stcentury.blogspot.com/2011/12/classification-of-libertarianism.html?showComment=1324413251211#c4718352180192394769

Fair enough. I do like to get these classifications right.

Ethical Theories: A Classification

Ethics is a confusing enough subject, and it takes much time and effort just to understand the various theories and their classification. The study of ethics can be divided into these three areas:

(1) Descriptive ethics, mere description of morality in different cultures;
(2) Normative ethics, the study of systems that dictate morally correct conduct;
(3) Metaethics, discussion of meanings of moral terms without directives.

We can provide the general classification of normative ethical theories here:

(1) Non-cognitivism

(1) Emotivism (Spinoza, Hume, C. L. Stevenson, A. J. Ayer)

(2) Prescriptivism (R. M. Hare)

(3) cognitivist expressivism (S. Blackburn; M. Timmons 1999; T. Horgan)

(2) Cognitivism

(i) Anti-realism

(a) Moral subjectivism

(b) Error theory

(ii) Moral realism

(a) Ethical naturalism

Utilitarianism

Non-theological natural rights theory

Thomism

neo-Aristotelian ethical naturalism (P. Foot; R. Hursthouse)

(b) Ethical non-naturalism

G. E. Moore ethical intuitionism/agathistic consequentialism

Platonist ethics

divine command ethics

Kantian ethics

I have made a more detailed list below of the major objective ethical theories and their classification.

(1) Deontological ethics

(a) Moral absolutism

(i) Divine Command Theory

(ii) Categorical Imperative ethics (Kantian ethics)

(b) Moral Universalism (minimal/moderate moral realism)

(i) Natural law theories (Plato and many Christian philosophers)

(ii) Natural rights theories

(iii) Thomist ethics

(iv) Pluralistic deontology, the non-absolutist ethics of W.D. Ross

(v) Human rights objectivism (Rawls)

(2) Teleological/Consequentialist ethics:

(a) Virtue Ethics

(i) Eudaemonist theories

(ii) Plato’s eudaemonist ethics

(iii) Aristotle’s eudaemonist ethics

(iv) Stoic ethics (with natural law)

(v) non-eudaemonist virtue ethics

(vi) agent-based virtue ethics of Michael Slote (2001)

(vii) neo-Aristotelian ethical naturalism (P. Foot; R. Hursthouse)

(b) Consequentialist (minimal/moderate moral realism)

(i) Utilitarian-type theories

- Hedonism

- egoism (the 17th-century English philosopher Thomas Hobbes)

- universal/universalistic hedonism = utilitarianism (Bentham, Mill, and Sidgwick): act utilitarianism, rule utilitarianism

(ii) Other teleological/utilitarian-type

- ideal-moral-code rule consequentialism (Hooker 2000; Richard Brandt)

- preference rule consequentialism (John Harsanyi)

- Motive consequentialism (Robert Adams)

- ideal consequentialism/utilitarianism (G.E. Moore; Hastings Rashdall)

- preference consequentialism/utilitarianism (R. M. Hare; Peter Singer)

- two-level preference consequentialism/utilitarianism (R. M. Hare)

- Negative consequentialism (Popper, Christoph Fehige and Clark Wolf)

- evolutionary ethics, with ends of action, survival and growth (Herbert Spencer) power, as in despotism (Niccolò Machiavelli and Friedrich Nietzsche)

- satisfaction and adjustment, pragmatism (Ralph Barton Perry and John Dewey)

- freedom, existentialism (Jean-Paul Sartre)

- Buddhist ethics

- Mohism (Mo Tzu/Micius)

- Ayn Rand’s objectivism?

(3) Ayn Rand’s objectivism?

(4) Utilitarian Kantian Principle of James Cornman (combines deontology and utilitarianism).

I will just make some quick remarks here.

Non-cognitivism
Non-cognitivism contends that moral statements do not express propositions and have no truth values.

Ethical non-naturalism
These theories include G. E. Moore’s intuitionism/agathistic consequentialism; Platonist ethics; divine command ethics, and Kantian ethics. Moral knowledge is a non-natural property known by (1) intuition, (2) god’s command or (3) a priori reasoning in these theories.

Naturalism
Ethical naturalism holds that moral knowledge is empirical in the sense that we can use the methods of the natural and social sciences to understand it. Moral concepts are reducible to, or definable in, non-ethical, natural terms. Most utilitarian theories are in the class of moral naturalism:

“even utilitarians who object to hedonism in its original, Benthamite form, as Mill expressly did, and utilitarians who stray even farther from the hedonistic fold, as I will suggest that Mill, perhaps unwittingly, also did, usually agree that the good is one or another kind of natural property. The dominant view, in other words, is that whatever is intrinsically good is part of nature. It is therefore fair to say that, with very few exceptions, utilitarians are ethical naturalists. One can be a utilitarian, though, and not be an ethical naturalist. For example, G. E. Moore, one of the founders modern analytic philosophy, was a utilitarian. He was as committed as Bentham or Mill to enhancing overall goodness by maximizing social utility, taking social utility to be the logical sum of individuals’ utilities. However, Moore famously opposed ethical naturalism, insisting that the very idea rest on what he disparagingly called the ‘naturalistic fallacy’. In direct opposition to Mill, Moore maintained that the good can only be a non natural property...” (Levine 2002: 136).

According to Moore, all naturalist ethical theories commit the naturalistic fallacy.

The deontological theories (or duty/obligation based morality) hold that the basis of morality is duty and some acts are always right no matter what consequences they can cause (the best example of which is Kantian ethics or some forms of divine command theory; Kant famously said that it is always wrong to lie, no matter what the circumstances).

The Eudaemonist theories of ethics are those that hold that morality consists in some activity appropriate to man as a human being, and thus tend to emphasize the cultivation of virtue or excellence as the end of our action or moral life. These theories were mainly held by the ancient Greeks and Romans.

The utilitarian theories hold that utility/happiness is the end we should aim at, and the rightness or wrongness of an action is judged by ability to create more utility/happiness in the world.

Consequentialist theories hold that other ends are also important, and not just utility.

BIBLIOGRAPHY

Hooker, B. 2000. Ideal Code, Real World: A Rule-Consequentialist Theory of Morality, Oxford University Press, Oxford, England and New York.

Levine, A. 2002. Engaging Political Philosophy: From Hobbes to Rawls, Blackwell, Malden, Mass.